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Title: Composite functions and their differentiation
Description: Comprehensive notes and practical problems and solutions) covering: -Full derivative -Set function
Description: Comprehensive notes and practical problems and solutions) covering: -Full derivative -Set function
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A composite function of two
variables is a function whose
one or both arguments are
functions of other arguments
...
Since the independent
variable is one, such a
function can be called a
function of one variable t
...
dt
The derivative of such a
function is found by the
formula:
dz z dx z dy
...
Given the previous formula,
the derivative will be equal to:
dz z dx z dy
...
b) a composite function of two
intermediate variables u and
v, each of which is a function
of two independent variables
x and y:
z f (u; v), where
u u(x; y), v v(x; y)
...
y u y v y
Set function:
y (tgx)
sin x
'
x
...
Answer:
y (tgx)
'
x
sin x
1
ln(tgx) cos x
...
2
2
Title: Composite functions and their differentiation
Description: Comprehensive notes and practical problems and solutions) covering: -Full derivative -Set function
Description: Comprehensive notes and practical problems and solutions) covering: -Full derivative -Set function